Stability and Sensitivity Analysis in Convex Vector Optimization

In this paper stability and sensitivity of the efficient set in convex vector optimization are considered. The perturbation map is defined as a set-valued map which associates, with each parameter vector, the set of all minimal points of the parametrized feasible set with respect to an ordering cone in the objective space. Sufficient conditions for the upper and lower semicontinuity of the perturbation map are obtained. Because of the convexity assumptions, the conditions obtained are fairly simple if compared with those in the general case. Moreover, a complete characterization of the contingent derivative of the perturbation map is obtained under some assumptions. It provides a quantitative information on the behavior of the perturbation map and allows to investigate the sensitivity of the efficient set with respect to the perturbations of the problem parameters

Sensitivity Analysis in Multiobjective Optimization

Sensitivity analysis is both theoretically and practically useful in optimization. However, only a few results in this direction have been obtained for multiobjective optimization. In this paper, the issue of sensitivity analysis in multiobjective optimization is dealt with. Given a family of parametrized multiobjective optimization problems, the perturbation map is defined as the set-valued map which associates to each parameter value the set of minimal points of the perturbed feasible set with respect to a fixed ordering convex cone. The behavior of the perturbation map is analyzed quantitatively by using the concept of contingent derivative for set-valued maps. Particularly it is shown that the contingent derivative of the perturbation map for multiobjective programming problems with parametrized inequality Constraints is closely related to the corresponding Lagrange multipliers

Consideration on Supremum in a Multidimensional Space and Conjugate Duality in Multiobjective Optimization

The first part of this paper is devoted to consideration on the definition of "supremum" in a multi-dimensional Euclidean space. A desirable definition is looked for among several possible alternatives. In the second part conjugate duality in multiobjective optimization is developed. Supremum is defined in the extended multi-dimensional Euclidean space on the basis of consideration in the first part. Some useful concepts such as conjugate maps and subgradients are introduced for vector-valued set-valued maps. Finally a strong duality result for a multiobjective optimization problem is proved under a regularity condition

Optimality and Duality for Nonsmooth Multiobjective Fractional Programming with Generalized Invexity

AbstractIn this paper, we consider a class of nonsmooth multiobjective fractional programming problems in which functions are locally Lipschitz. We establish generalized Karush–Kuhn–Tucker necessary and sufficient optimality conditions and derive duality theorems for nonsmooth multiobjective fractional programming problems containing V-ρ-invex functions

Laboratory investigation of lateral dispersion within dense arrays of randomly distributed cylinders at transitional Reynolds number

Published versio

Comparative Studies on Short and Long Length-Scale Stall Cell Propagation in an Axial Compressor Rotor

Abstract In a low-speed compressor test rig at Kyushu University, multiple short length-scale stall cells appeared under a mild stall condition and turned into a long length-scale cell under a deep stall condition. Then, for the both types of stall cell, the pressure distribution on the casing wall and the velocity distributions upstream and downstream of the rotor have been measured by high response pressure transducers and a slanted hot-wire, respectively. The time-dependent ensemble averages of these distributions have been obtained phase-locking to both of the rotor and the stall cell rotation by using a so-called 'double phase-locked averaging technique' developed by the authors. Structure of the two stall cells are compared with each other: The short length-scale stall cell is characterized by a concentrated vortex spanning from the casing wall ahead of the rotor to the blade suction surface. In the long length-scale stall cell, the separation vortices go upstream irregularly when blade separation develops in the front half of the cell, and reenter the rotor on the hub side in the rear half of it. The unsteady aerodynamic force and torsional moment acting on the blade tip section have been evaluated from the time-dependent ensemble averages of the casing wall pressure distribution. The force fluctuation due to the short length-scale cells is somewhat smaller than that for the long length-scale cell. The blade suffers two peaks of the force during a period of the short length-scale cells passing through it. The moment fluctuation for the short length-scale cells is considerably larger than that for the long length-scale cell

Theory of the beta-type Organic Superconductivity under Uniaxial Compression

We study theoretically the shift of the superconducting transition temperature (Tc) under uniaxial compression in beta-type organic superconductors, beta-(BEDT-TTF)2I3 and beta-(BDA-TTP)2X[X=SbF6,AsF6], in order to clarify the electron correlation, the spin frustration and the effect of dimerization. The transfer integrals are calculated by the extended Huckel method assuming the uniaxial strain and the superconducting state mediated by the spin fluctuation is solved using Eliashberg's equation with the fluctuation-exchange approximation. The calculation is carried out on both the dimerized (one-band) and nondimerized (two-band) Hubbard models. We have found that (i) the behavior of Tc in beta-(BEDT-TTF)2I3 with a stronger dimerization is well reproduced by the dimer model, while that in weakly dimerized beta-BDA-TTP salts is rather well reproduced by the two-band model, and (ii) the competition between the spin frustration and the effect induced by the fluctuation is important in these materials, which causes nonmonotonic shift of Tc against uniaxial compression.Comment: 18 pages, 16 figures, 2 tabl

Exchange flow between open water and floating vegetation

This study describes the exchange flow between a region with open water and a region with a partial-depth porous obstruction, which represents the thermally-driven exchange that occurs between open water and floating vegetation. The partial-depth porous obstruction represents the root layer, which does not penetrate to the bed. Initially, a vertical wall separates the two regions, with fluid of higher density in the obstructed region and fluid of lower density in the open region. This density difference represents the influence of differential solar heating due to shading by the vegetation. For a range of root density and root depths, the velocity distribution is measured in the lab using PIV. When the vertical wall is removed, the less dense water flows into the obstructed region at the surface. This surface flow bifurcates into two layers, one flowing directly through the root layer and one flowing beneath the root layer. A flow directed out of the vegetated region occurs at the bed. A model is developed that predicts the flow rates within each layer based on energy considerations. The experiments and model together suggest that at time- and length-scales relevant to the field, the flow structure for any root layer porosity approaches that of a fully blocked layer, for which the exchange flow occurs only beneath the root layer.National Science Foundation (U.S.) (grant EAR0509658

Efficiency Assessment of Using Flammable Compounds from Water Treatment and Methanol Production Waste for Plasma Synthesis of Iron-Containing Pigments

This article describes the possibility of applying the low-temperature plasma for obtaining iron-containing pigments from water purification and flammable methanol production waste. In this paper were calculated combustion parameters of water-saltorganic compositions (WSOC) with different consists. Authors determined the modes of energy- efficient processing of the previously mentioned waste in an air plasma. Having considered the obtained results there were carried out experiments with flammable dispersed water-saltorganic compositions on laboratory plasma stand. All the experimental results are confirmed by calculations